Piecewise-analytic interfaces with weakly singular points of arbitrary order always scatter

Abstract

It is proved that an inhomogeneous medium whose boundary contains a weakly singular point of arbitrary order scatters every incoming wave. Similarly, a compactly supported source term with weakly singular points on the boundary always radiates acoustic waves. These results imply the absence of non-scattering energies and non-radiating sources in a domain whose boundary is piecewise analytic but not infinitely smooth. Local uniqueness results with a single far-field pattern are obtained for inverse source and inverse medium scattering problems. Our arguments provide a rather weak condition on scattering interfaces and refractive index functions to guarantee the scattering phenomena that the scattered fields cannot vanish identically.